# Unraveling the effects of multiscale network entanglement on disintegration of empirical systems

arXiv: https://arxiv.org/abs/2008.05368 · HTML: https://mlsanity.com/paper/2008.05368/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [DASentimental: Detecting depression, anxiety and stress in texts via emotional recall, cognitive networks and machine learning](https://mlsanity.com/paper/2110.13710/) (2021)
- [Influential Simplices Mining via Simplicial Convolutional Network](https://mlsanity.com/paper/2307.05841/) (2023)

## Abstract (arXiv)

Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks ---i.e. the capacity of a network to maintain its integrity under removal of nodes or links. Here, we introduce network entanglement to study network robustness through a multi-scale lens, encoded by the time required to diffuse information through the system. Our measure's foundation lies upon a recently proposed framework, manifestly inspired by quantum statistical physics, where networks are interpreted as collections of entangled units and can be characterized by Gibbsian-like density matrices. We show that at the smallest temporal scales entanglement reduces to node degree, whereas at the large scale we show its ability to measure the role played by each node in network integrity. At the meso-scale, entanglement incorporates information beyond the structure, such as system's transport properties. As an application, we show that network dismantling of empirical social, biological and transportation systems unveils the existence of a optimal temporal scale driving the network to disintegration. Our results open the door for novel multi-scale analysis of network contraction process and its impact on dynamical processes.